Computational Investigation on the Formation and Decomposition Reactions of the C4H3O Compound.

Gas-phase mechanism and kinetics of the formation and decomposition reactions of the C4H3O compound, a crucial intermediate of the atmospheric and combustion chemistry, were investigated using ab initio molecular orbital theory and the very expensive coupled-cluster CCSD(T)/CBS(T,Q,5)//B3LYP/6-311++G(3df,2p) method together with transition state theory and Rice-Ramsperger-Kassel-Macus kinetic predictions. The potential energy surface established shows that the C3H3 + CO addition reaction has four main entrances in which C3H3 + CO → IS1-cis (CHCCH2CO) is the most energetically favorable channel. The calculated results revealed that the bimolecular rate constants are positively dependent on both temperatures (T = 300-2000 K) and pressures (P = 1-76,000 Torr). Of these values, the k 1 rate constant of the C3H3 + CO → IS1-cis addition channel is dominant over the 300-2000 K temperature range, increasing from 1.53 × 10-20 to 1.04 × 10-13 cm3 molecule-1 s-1 with the branching ratio reducing from 62% to 44%. The predicted unimolecular rate coefficients in the ranges of T = 300-2000 K and P = 1-76,000 Torr revealed that the intermediate products IS1-cis , IS1-trans , and IS2 are rather unstable and would rapidly decompose back to the reactants (C3H3 + CO), especially at high temperatures (T > 1000 K). The high-pressure limit rate constants for the C4H3O decomposition leading to products (C3H3 + CO), (CHCCHCO + H), and (CHCO + C2H2) have been found to be in excellent agreement with the available literature values proposed by Tian et al. (Combust. Flame, 2011, 158, 756-773) without any adjustment from the ab initio calculations. Therefore, the predicted temperature- and pressure-dependent rate constants can be confidently used for modeling CO-related systems under atmospheric and combustion conditions.

Introduction

Carbon monoxide is present in the environment and is known as the silent killer. It can be found in fumes generated from burning fuel in cars or trucks, small engines, stoves, lanterns, grills, fireplaces, or furnaces.[1] The CO gas can build up indoors and poison people and animals who breathe it.[2] The most common symptoms of CO <span class="Disease">poisoning are headache, dizziness, weakness, upset stomach, vomiting, chest pain, and confusion.[3] Exposure to carbon monoxide may cause significant damage to the heart and central nervous system, especially to the globus pallidus.[4] People who are sleeping or drunk can die from CO poisoning before they have symptoms. In terms of structure, CO contains one carbon atom and one oxygen atom, connected by a triple bond including two π bonds and one σ bond, with the C≡O bond length of 112.8 pm.[5]

The addition of alkyl radicals to <span class="Chemical">carbon monoxide and the dissociation of acyl-free radicals into alkyl radicals and CO form an important class of bimolecular and unimolecular reactions.[6−9] The mechanism and kinetics for these reactions are fundamental to understanding the complex processes occurring in pyrolysis, combustion, and photochemical reactions. However, these reactions have received little study both experimentally and theoretically. Only the CH3 + CO and C2H5 + CO additions and/or the dissociations of CH3CO and C2H5CO have been studied by several authors,[10−14] while the C3H3 + CO addition and the decomposition of the C3H3CO radicals have not been reported yet.

Although having no data on the C3H3 + CO system, the addition of a <span class="Chemical">propargyl radical to carbon monoxide can be predicted to produce vibrationally excited buta-2,3-dien-1-one which has a chemical formula CH2=C=CH–C*=O and/or CH≡C–CH2–C*=O, as shown in reaction 1. These excited species may then be stabilized by collisional energy transfer, reaction 2, or they can decompose back into propargyl radicals and carbon monoxide, reaction 3. This system is actually a chemical activation system where the unimolecular decomposition of buta-2,3-dien-1-one is the reverse of the addition of the propargyl radical to carbon monoxide.

To the best of our knowledge, so far, the bimolecular rate constants for the addition of propargyl radicals to <span class="Chemical">carbon monoxide have not been calculated and/or measured previously. Only several investigations of Clavert and co-workers (1958 and 1965),[10,12] Kerr and Lloyd (1967),[13] and Watkins and Thompson (1973)[14] reported their rate constants for the addition of methyl and ethyl radicals to carbon monoxide; where the activation energies were found to be 3.9 and 4.8 ± 0.1 kcal/mol, respectively. These values are estimated to be relatively smaller than the activation energy predicted for the C3H3 + CO → C3H3CO reaction because both methyl and ethyl radicals are more reactive than the propargyl radical. Watkins and Thompson also indicated that the activation energy for ethyl addition to CO is significantly lower than that for the addition to C2H4. Accordingly, they concluded that carbon monoxide was more reactive toward free radicals than were many olefins. Therefore, it can be anticipated that the addition reactions of methyl and ethyl radicals to carbon monoxide that formed acetyl radical and propionyl radical are also similar to the buta-2,3-dien-1-one formation reactions from C3H3 and CO.

Due to the lack of information for the C3H3 + CO addition, important reaction in combustion chemistry, as well as the dissociation of the <span class="Chemical">C3H3CO radicals, in this study, we report the detailed mechanisms and the effect of temperatures (T = 300–2000 K) and pressures (P = 1 to 76,000 Torr) on the kinetics of propargyl radical addition to carbon monoxide and present information on the nonequilibrium dissociation of the C3H3CO radicals. In order to compare the reactive ability of different alkyl radicals with the closed-shell species such as CO and NH3, the calculated results have also been compared with the available experimental data for the CH3 + CO and C2H5 + CO systems as well as the previously predicted values for the C3H3 addition to ammonia.

Quantum Chemical Methodology

In this study, the DFT method with the Becke three-parameter exchange and Lee–Yang–Parr correlation (B3LYP) hybrid functional[15−17] in conjunction with the Pople 6-311++G(3df,2p)[18] basis set was employed for geometry optimization of all species involving in the reaction of the <span class="Chemical">C3H3 radical with the CO molecule. The needed parameters for energy and kinetic calculations including harmonic vibrational frequencies, moments of inertia, rotational constants, and zero-point vibrational energies (ZPVEs) were also computed at the B3LYP/6-311++G(3df,2p) level. The ZPVEs were subsequently corrected by a 0.971 parameter to receive the reliable energies for all species as shown in several prior investigations.[19−24] All the stationary points on the potential energy surface (PES) are distinguished from each other by their harmonic vibrational frequencies where the local minima including the reactants, intermediates, and products contain all positive vibrational frequencies, while a saddle point holds a single imaginary frequency in addition to real frequencies. The connection of a located saddle point of an elementary reaction on the obtained PES with two assumed minima has been confirmed by the intrinsic reaction coordinate (IRC) method[25,26] carried out at the B3LYP/6-311++G(3df,2p) level of theory.

The single-point electronic energies for all species were then calculated by using the coupled cluster with single, double, and triple perturbative excitations [CCSD(T)][27] together with the correlation consistent basis sets of Dunning and coworkers known as the doubly augmented basis sets (d-aug-cc-pVXZ, X = T, Q, and 5)[28] w<span class="Chemical">hich were extrapolated to the complete basis set (CBS) limit and corrected with ZPVEs. The extrapolation formula of Feller[29] (i) was utilized for the Hartree–Fock energies, while electron correlation energies were extrapolated separately according to the three-parameter expression with the integer exponents of Martin[30] (ii). All the B3LYP/6-311++G(3df,2p) optimizations and the CCSD(T)/CBS single-point energy calculations were carried out utilizing Gaussian 16 software.[31]where m equals 2, 3, 4, and 5 for double, triple, quadruple, and quintuple zeta basis functions, respectively. The asymptotic values ECBS and ECBS′ stand for the Hartree–Fock and correlation energies, respectively, and they are obtained according to three-point extrapolation results using the d-aug-cc-pVTZ, d-aug-cc-pVQZ, and d-aug-cc-pV5Z basis sets.

For the kinetic treatments, the transition state theory (TST)[32,33] and the microcanonical Rice–Ramsperger–Kassel–Marcus (RRKM) theory[34−37] have been adopted to compute rate coefficients for the bimolecular C3H3 + CO additions and the unimolecular buta-2,3-dien-1-one decompositions, utilizing the ChemRate code[38] and the MESMER program,[39] respectively. The needed parameters such as activation energies of elementary reactions on the PES, moments of inertia, and vibrational frequencies of geometric structures involved were taken into employment as initial values for computations of the density of states and the sum of states relied on the Stein–Rabinovitch version of the Beyer–Swineheart algorithm.[40,41] In the RRKM calculations, the unimolecular rate coefficients were predicted by solving the master equation (ME), using an energy grain size of 100 cm–1. The calculated sum of states and density of states from the microcanonical process were utilized to run the ME code for unimolecular rate coefficients. For the reaction channels concerning H-shift, Eckart tunneling corrections[42] were taken into consideration in the rate coefficient calculations. The low-frequency vibrational modes situated at the single bonds were treated as hindered internal rotors (HIRs), where the hindrance potentials, V(θ), as a function of torsional angle, θ, along the single bonds were explicitly obtained at the B3LYP/6-311++G(3df,2p) level via relaxed surface scans with the step size of 10° for dihedral angles corresponding to the rotations. The torsional potential for the HIR of the intermediate states including cis-HCCCH2CO, trans-HCCCH2CO, CH2CCHCO, and HCCCHCHO are shown in Figure S3 in Supporting Information. Ar was employed as the bath gas, and the energy-transfer exponential down model, ⟨ΔE⟩down = 75 × (T/300)1.05 cm–1.[43] The L-J parameters for Ar (ε/kB = 113.50 K; σ = 3.465 Å) were taken from the literature,[44] while ε/kB = 224.7 K and σ = 4.162 Å[45] were applied for the C4H3O isomers. The rate constants were calculated over the 300–2000 K temperature range and pressures of 1–76,000 Torr. The relative energies of all species involved at the UCCSD(T)/CBS//B3LYP/6-311++G(3df,2p) level were used for the rate-constant predictions.

Results and Discussion

The PES of the propargyl radical addition to CO and the <span class="Chemical">C4H3O decomposition obtained at the UCCSD(T)/CBS//B3LYP/6-311++G(3df,2p) + ZPVE level of theory is graphically plotted, as shown in Figure . The relative energy values displayed on the PES have the error margins of about ±1.0 kcal/mol corresponding to that expected for the CCSD(T)/CBS method.[46,47] The harmonic vibrational frequencies, Cartesian coordinates, energies, and geometric structures of all species (the reactants, intermediates, transition states, and products) on the PES optimized at the B3LYP/6-311++G(3df,2p) level are shown in Tables S1–S3 and Figures S1 and S2, respectively, in Supporting Information. The reaction energies calculated at the UCCSD(T)/CBS(T,Q,5) level have been compared with the experimentally reported values derived from ATcT as presented in Table S4 in Supporting Information. It is evident from Table S4 that the computed values for some reactions are in excellent agreement with the available literature data within their deviations, for example, the maximum deviation of our values compared with ATcT is around 1.0 kcal/mol. Such good accordance with the computed relative energies shows that the UCCSD(T)/CBS(T,Q,5) method is the best choice for the C4H3O system.

Figure 1

PES of the C3H3 + CO reaction at the CCSD(T)/CBS//B3LYP/6-311++G(3df,2p) + ZPVE level of theory. (Energies are in kcal/mol).

The T1 diagnostic analysis[48] of all species including reactants, products, transition states, and intermediate states of the C4H3O system is presented in Table S5 in Supporting Information. The calculated results reveal that the T1 diagnostics of all stationary points on the PES have insignificant multireference characters because all the T1 values are less than the threshold for T1 diagnostics of the closed-shell and open-shell species w<span class="Chemical">hich are 0.02 and 0.045,[49] respectively, indicating that the CCSD(T) method is suitable for the present work.

The PES illustrated in Figure shows that the reaction of C3H3 with CO can occur via addition directions leading to three adducts, namely IS1-, IS1-, and <span class="Chemical">IS2. From these adducts, various intermediate states and bimolecular products have been created. Figure shows that the CO molecule can attack the CH2=C=CH radical at the two terminal C atoms to produce isomers of C4H3O. It is worth noting that we failed many times to find a transition state for the CO addition to the central C atom; therefore, we anticipate that it is very difficult to form a chemical bond between CO and the central C atom of the propargyl radical because CO is a stable species and the central C atom of the propargyl radical is considered to be saturated with valence. The two isomers IS1- and IS1- were formed when CO attacks the CH2 carbon atom in two different directions, for which the C3H3 + CO → IS1-cis and C3H3 + CO → IS1-trans processes have to surpass the transition states TS1 and TS2 with barrier energies of nearly 13 and 14 kcal/mol, respectively. In the TS1 structure shown in Figure , the CO molecule appears close to the CH2 group at a distance of 2.013 Å while the ∠CCC bond angle of C3H3 reduces about 4° to facilitate the formation of a new CH2–CO bond, resulting in the IS1- adduct whose relative energy is 5.0 kcal/mol.

Figure 2

Some main geometric structures on the PES of the C3H3 + CO system optimized at the B3LYP/6-311++G(3df,2p) level of theory. The bond lengths and bond angles are in units of angstrom and degree, respectively.

Similarly, in the TS2 geometry, the loose CH2–CO bond is slightly longer than that of TS1, being 2.017 Å. However, the ∠CCC bond angle decreases only 2°, and the CO molecule attacks in the reverse direction with the CO direction of the TS1 structure, leading to another adduct denoted as IS1- with a relative energy of approximately 5.2 kcal/mol. Both TS1 and TS2 have only one negative frequency, indicating that they are first-order saddle points on the PES. The IRC scan results of these two TSs shown in Figure S4 reveal that TS1 connects between the reactants and IS1-, while TS2 is a bridge of the reactants with IS1-.

In contrast, only one intermediate state, namely, IS2 was generated when CO attacks the CH <span class="Chemical">carbon atom of the propargyl radical via two transition states TS3 and TS4 located at the energy level of around 14 and 16 kcal/mol, respectively. The structures of TS3 and TS4 shown in Figure indicate that the attack directions of CO in these structures are similar to those in the TS1 and TS2 structures, respectively. Nevertheless, both these transition states lead to the same structure instead of two different types of cis and trans as produced in the cases of TS1 and TS2. For comparison, the energy level of IS2 is equivalent to those of IS1- and IS1- (E = 5.2 vs 5.0 and 5.2 kcal/mol), but their geometric structures are quite different. Particularly, in the structures of IS1- and IS1-, the ∠CCO bond angles are ∼130 and ∼126°, respectively, while that of the IS2 geometry is nearly 180°. In contrast, the ∠CCC bond angles of IS1- and IS1- have the same value of 180°, whereas the ∠CCC bond angle of IS2 holds the value of 144.6°, suggesting that there is a single electron in an orbital of the central carbon atom of the HC–C–CH2 chain. Thus, it can be said that after interaction with carbon monoxide at the position of the CH group forming the IS2 structure, the central carbon atom of the propargyl radical has changed from the sp-hybridized state to the sp2-hybridized state. In contrast, the sp-hybridized state of the C atom was still unchanged as proceeding from C3H3 to the structures of IS1- and IS1-. Figure shows that all four isomers of C4H3O have a comparable formation probability because the energy barriers of the four corresponding reaction paths giving IS1-, IS1-, and IS2 are more or less the same level. The difference between them is only 1–3 kcal/mol, ranging from well over 13 to just under 16 kcal/mol. The formation probability of these isomers will be counted in the kinetic section.

After forming IS1- and IS1-, the bimolecular and unimolecular products P2 and IS9, respectively, can be indirectly and/or directly generated, in which the P2 (HCCCHCO + H) product is formed when IS1- proceeds via two transition states (TS12 and TS22) and one intermediate state IS3, while the IS9 intermediate product was directly produced as IS1- proceeded through only one transition state TS18. In the channel, IS1- → IS3- → P2, the first step is a 2,1-H-shift process producing IS3- (HCCCHCHO) located at nearly 1.1 kcal/mol above the reactants, followed by an H-abstraction process in the second step creating the P2 product situated at the 42.5 kcal/mol energy level. Transition state TS12 of the first step holds an imaginary frequency of 1589i cm–1, which correctly reflects the movement of a H atom whereas the 678i cm–1 imaginary frequency of TS22 corresponds to the H-abstraction of the CHO group at a C–H distance of about 2.0 Å and the increase of the ∠CCO bond angle from 124.8 to ∼169°, cf. Figure S2. In the IS1- → IS9 channel, saddle point TS18 with a negative frequency of 584i cm–1 displays a four-membered carbon ring formation with a C–C distance recorded to be 2.055 Å. It should be noted that the P2 product can be directly created from IS5 as proceeding via the TS23 transition state whose relative energy is ∼45 kcal/mol.

From IS2 (<span class="Chemical">CH2CCHCO), many other intermediates and products can be formed directly or indirectly. Of these products, the P1 (H2CCC + HCO) product was formed when IS2 surpassed via tight transition state TS6 to form IS6 before carrying out the barrierless process from IS6 to P1. The tight TS identified by a 1515i cm–1 imaginary frequency is in reasonable agreement with an H-shift process between two adjacent carbon atoms. Therefore, the geometric structure of TS6 shown in Figure S2 with the loose bond lengths C(2)–H and C(1)–H of 1.716 and 1.105 Å, respectively, confirms that the 2,1-H-migration will create the IS6 (H2CCCCHO) intermediate though the C(2)–C(1) bond length of 2.143 Å is significantly longer than the C–C single bond of any organic compound. The C(2)–C(1) bond length was reduced to 1.424 Å in the structure of IS6 and was then broken to release the separated HCO and H2CCC groups in the P1 product. If the IS2 → IS6 isomerization step has to overcome an energy barrier of 73.7 kcal/mol at TS6, the IS6 → P1 dissociation step needs to receive a 79.6 kcal/mol energy. The P3 (HCCCCO + H2) product was produced directly from the IS2 → P3 one-step process via the TS17 saddle point standing at the 88.7 kcal/mol energy level above the entrance point. In the TS17 structure, two H atoms at the CH and CH2 groups are abstracting at the distances of 1.639 and 1.425 Å, respectively, while the bond angle reduced about 28.5° to facilitate the abstraction of the two H atoms. These hydrogen atoms then combined with each other to create a H2 molecule in the P3 product. The 88.7 kcal/mol relative energy of TS17 (1644i cm–1) shows that the IS2 → P3 channel hardly occurs at the normal condition of temperature and pressure. Although P3 is considered to be the most thermodynamically stable product, it still lies ∼35 kcal/mol above the starting point. To form the bimolecular product, P4 (HCCO + HCCH), the IS2 adduct must proceed via the tight transition states, namely, TS10 and TS19, for which the first TS belongs to the IS2 → IS5 isomerization process and the second one for the IS5 → P4 decomposition channel. The first process displays an H-shift from the CH2 group to the adjacent single carbon atom of IS2 (CH2=C=CHCO) forming the IS5 (CHCHCHCO) isomer. The loose bond lengths of C(4)–H and C(3)–H in the TS10 structure optimized at the B3LYP/6-311++G(3df,2p) level are 1.322 and 1.262 Å, respectively, and the corresponding imaginary frequency is 1793i cm–1, showing one typical H-shift TS whose energy barrier is nearly 50 kcal/mol. The second process shows the C(2)–C(3) bond scission via the TS19 saddle point at a distance of 2.226 Å, giving rise to acetylene molecule (C2H2) and ketenyl radical (HCCO). The CCSD(T)/CBS energy value of TS19 relative to the P4 (40.68 kcal/mol) product is about 5.2 kcal/mol, which is in good agreement with the values of 4.4 and 5.3 kcal/mol calculated at the G3B3//B3LYP/6-311++G(d,p) and G3B3//QCISD/6-31G(d) levels, respectively, by Xie at al.[50] Similar to the formation of P3, the P5 product was also created directly by the one-step process, IS2 → P5, via the TS15 first-order transition state holding one imaginary frequency of 252i cm–1, corresponding to an H-abstraction from the CH group at a long distance of 2.166 Å. Compared to the P3 product, P5 is more favorable because the energy barrier of the IS2 → P5 process is about 38 kcal/mol lower than that of the IS2 → P3 process. However, P3 is more stable than P5, E = 35.1 versus 46.7 kcal/mol, because the closed-shell species HCCCCO and H2 in P3 have been known to be well constructed than the open-shell ones H2CCCCO and H in P5. In a similar trend as P4, the P6 product was formed when IS2 proceeded across via the TS9 and TS21 saddle points where TS9 (2353i cm–1) is a bridge between the IS2 (CH2CCHCO) and IS4 (CH2CCCOH) intermediates, describing an H-transfer process from the CH group to the oxygen atom with the vdW bond lengths C–H and H–O of 1.267 and 1.555 Å, respectively. The energy barrier height of TS9 is larger than that of TS10 by about 24 kcal/mol, indicating that P4 (HCCO + C2H2) is made easily than P6 (HCCCC + H2O). The TS21 (973i cm–1) transition state illustrates simultaneously two processes of an H-shift from the CH2 group to the OH group and a C–OH2 bond breaking. Therefore, the activation energy required to supply for the IS4 → P6 process is fairly high, being about 74 kcal/mol. Figure shows that the formation of the P6 product from the C3H3 + CO entrance channel is an endothermic process by ∼79 kcal/mol. Last but not least, radical product P7 (C2H3 + CCO) was formed by the same process as the formation of the P1 (H2CCC + HCO) product. At the isomerization step, IS2 → IS7, the TS16 transition state identified by a 1430i cm–1 imaginary frequency describes a 2,3-H transfer with the distances C(2)–H and H–C(3) of 1.242 and 1.395 Å, respectively. The relative energy of TS16 (48.3 kcal/mol) is significantly lower than that of TS6 (∼79 kcal/mol), proving that the IS7 intermediate is more advantageous than the IS6 isomer. In terms of energy, IS7 is the most stable species on the PES of the C3H3 + CO system, whose energy is approximately 3.5 kcal/mol under the reactants. Whereas, the second step from IS7 to P7 was not confirmed by any well-defined transition state, which is similar to the IS6 → P1 channel. However, the dissociation energy of IS7 is much larger than that of IS6, E = 106 versus 79.5 kcal/mol, which makes the P7 product less stable in comparison with all other products of the title reaction. In addition to the seven products mentioned above, another product (C4H2 + OH) was also generated (see the full PES plotted in Figure S5 in Supporting Information). However, the energy barrier of the channel forming this bimolecular product is so high, being about 103 kcal/mol. It is easy to see that its contribution to the product formation of the reaction system is minor, and it --is not thus considered in detail in this text.

As stated above, although various intermediate states and bimolecular products can be formed from three adducts IS1-, IS1-, and IS2, the energy barriers of reaction channels forming these intermediates and products are so <span class="Chemical">high that they are not easily generated under ambient conditions, and they should not be considered in the kinetic calculations for the C3H3 + CO bimolecular reaction. Only four entrance reaction paths forming the three adducts mentioned above are energetically and kinetically favorable channels; therefore, in the kinetic sections hereafter, we totally focus on these channels.

Rate Constant Calculations

The rate constants of the C3H3 + CO reaction have been computed by the TST[32,33,9] approach using the ChemRate code. As stated previously, the reaction paths producing the IS1-, IS1-, and <span class="Chemical">IS2 intermediates are the favorable processes in terms of activation energy. The presence of other channels (see Figure ) is inconsequential to the kinetics of the C3H3 + CO reaction. Therefore, the low-lying channels utilized for rate-coefficient predictions can be presented by following four reactions

The individual rate constants of these channels denoted as k1–k4 and the total rate constant ktotal in the 300–2000 K temperature range and 760 Torr (Ar) are listed in Table and are graphically plotted as shown in Figure . It can be seen from this figure and Table , the k1 rate constant is the highest in the temperature range observed; its rate constants increase quickly from 1.53 × 10–20 cm3 molecule–1 s–1 at 300 K to 1.04 × 10–13 cm3 molecule–1 s–1 at 2000 K, followed by the values of k2 and k3 rising from 7.8 × 10–21 to 7.73 × 10–14 and from 1.66 × 10–21 to 5.5 × 10–14 cm3 molecule–1 s–1, respectively.

Table 1

Bimolecular Rate Constants (in Units of cm3 molecule–1 s–1) of the C3H3 + CO Reaction in the 300–2000 K Temperature Range at 760 Torr (Ar)

T (K)	k1	k2	k3	k4	ktotal
300	1.53 × 10–20	7.8 × 10–21	1.66 × 10–21	3.73 × 10–25	2.48E-20
400	3.08 × 10–18	1.87 × 10–18	6.05 × 10–19	2.83 × 10–22	5.55 × 10–18
500	5.47 × 10–17	3.53 × 10–17	1.56 × 10–17	1.16 × 10–20	1.06 × 10–16
600	3.13 × 10–16	2.08 × 10–16	1.1 × 10–16	1.07 × 10–19	6.31 × 10–16
700	1.01 × 10–15	6.82 × 10–16	4.01 × 10–16	4.52 × 10–19	2.09 × 10–15
800	2.36 × 10–15	1.62 × 10–15	1.01 × 10–15	1.25 × 10–18	4.99 × 10–15
900	4.54 × 10–15	3.16 × 10–15	2.04 × 10–15	2.67 × 10–18	9.74 × 10–15
1000	7.68 × 10–15	5.41 × 10–15	3.58 × 10–15	4.86 × 10–18	1.67 × 10–14
1100	1.19 × 10–14	8.44 × 10–15	5.68 × 10–15	7.93 × 10–18	2.60 × 10–14
1200	1.72 × 10–14	1.23 × 10–14	8.39 × 10–15	1.2 × 10–17	3.79 × 10–14
1300	2.37 × 10–14	1.71 × 10–14	1.17 × 10–14	1.7 × 10–17	5.25 × 10–14
1400	3.14 × 10–14	2.28 × 10–14	1.58 × 10–14	2.31 × 10–17	6.99 × 10–14
1500	4.03 × 10–14	2.94 × 10–14	2.05 × 10–14	3.04 × 10–17	9.02 × 10–14
1600	5.05 × 10–14	3.7 × 10–14	2.59 × 10–14	3.88 × 10–17	1.13 × 10–13
1700	6.19 × 10–14	4.56 × 10–14	3.21 × 10–14	4.83 × 10–17	1.40 × 10–13
1800	7.47 × 10–14	5.52 × 10–14	3.9 × 10–14	5.9 × 10–17	1.69 × 10–13
1900	8.87 × 10–14	6.57 × 10–14	4.66 × 10–14	7.1 × 10–17	2.01 × 10–13
2000	1.04 × 10–13	7.73 × 10–14	5.5 × 10–14	8.41 × 10–17	2.36 × 10–13

Figure 3

Rate constants of the C3H3 + CO reaction in the temperature range 300–2000 K at 760 Torr (Ar).

Although the k4 value increases with temperature in the 300–2000 K interval, from 3.73 × 10–25 to 8.41 × 10–17 cm3 molecule–1 s–1, its rate constant is about 3–5 orders of magnitude lower than that of k1; therefore, the C3H3 + CO → IS2 reaction path via TS4 can be considered to have a minor contribution to the total products. These calculated results have reflected exactly what happened in the PES mentioned above; it means that if TS1 < TS2 < TS3 < TS4, the values of k1, k2, k3, and k4 will follow the reverse orders.

The calculated branching ratio for the first channel (k1) forming IS1- holds the <span class="Chemical">highest percentage in the whole temperature range of 300–2000 K, gradually reducing from ∼62% at 300 K to ∼44% at 2000 K, while the yield for the third channel (k3) forming IS2 increases moderately from 6.7% at 300 K to well over 23% at 2000 K, cf. Figure . Unlike these two channels, the product yield of the second channel (k2) forming IS1- fluctuates with rising temperature; its percentage progresses from ∼31.5% at 300 K and reaches a maximum value of nearly 34% at 400 K before descending to 32.44% at both temperatures 900 and 1000 K. Then, the k2 branching ratio slowly increases again to 32.7% at 2000 K (see the purple line in Figure ). Not surprisingly, the branching ratio of the last channel does not exceed 0.04% over the studied range of 300–2000 K. This is rather reasonable because the k4 rate constant is much smaller than the values of k1, k2, and k3, cf. Table . The uncertainties of the calculated rate constants in the 300–2000 K range for k1, k2, k3, and k4 increase in the ranges of 1.9 × 10–20 to 8.96 × 10–15, 1.05 × 10–20 to 6.51 × 10–15, 8.68 × 10–22 to 2.23 × 10–15, and 6.46 × 10–25 to 8.72 × 10–18, respectively.

Figure 4

Branching ratios of the C3H3 + CO reaction in the temperature range 300–2000 K at 760 Torr (Ar).

The individual and total bimolecular rate constants of the four entrance channels mentioned above can be presented by the modified Arrhenius equation as follows

To the best of our knowledge, measurements and/or calculations of the rate coefficients for the addition of propargyl radicals to <span class="Chemical">carbon monoxide have not been reported previously. Therefore, no experimental data have been shown to compare with the present calculated results. However, it is interesting to compare the activation energy for the addition of the propargyl radical to carbon monoxide with that for ethyl and methyl additions which were found to be 4.8 ± 0.1 and 3.9 kcal/mol[14] at pressures of about 160–260 and 150 Torr, respectively. Apparently, the former addition is found to be significantly slower than the latter additions because the C3H3 + CO activation energy is about three to four times bigger than that of the C2H5 + CO and CH3 + CO addition reactions. Thus, it can be said that CO is more reactive toward free radicals C2H5 and CH3 than are propargyl radicals. Moreover, the calculated rate constants of the C3H3 + CO addition have been compared with those of the C3H3 + NH3 addition[51] at the same conditions of temperature and pressure as plotted in Figure .

Figure 5

Comparison of rate constants of the C3H3 + CO reaction with those of the C3H3 + NH3 reaction[51] in the temperature range 300–2000 K at 760 Torr (Ar).

Comparison of rate constants of the C3H3 + CO reaction with those of the <span class="Chemical">C3H3 + NH3 reaction[51] in the temperature range 300–2000 K at 760 Torr (Ar).

Figure shows that the total rate constants of the C3H3 + <span class="Chemical">NH3 system are significantly lower than those of the C3H3 + CO system. Especially at low temperatures (T ≤ 1000 K), the former values are approximately 3–9 orders of magnitude lower than the latter values, for example, the C3H3 + NH3 rate coefficients at 300 and 1000 K are 7.98 × 10–29 and 5.10 × 10–17 cm3 molecule–1 s–1, respectively, while the C3H3 + CO values at the corresponding temperatures are 2.48 × 10–20 and 1.67 × 10–14 cm3 molecule–1 s–1. However, at higher temperatures (T > 1000 K), the deviation between these values is shortened to about 2 orders of magnitude, for example, 7.09 × 10–15 compared to 2.36 × 10–13 cm3 molecule–1 s–1 at 2000 K. It can be explained that the values of the C3H3 + NH3 system are much smaller than the C3H3 + CO values because the mechanism of the former outstood the H-abstraction processes whose average energy barrier is about 25 kcal/mol[51] calculated at the CCSD(T)/6-311++G(3df,2p)//B3LYP/6-311++G(3df,2p) level, while the addition processes are dominant at the latter system whose average energy barrier is ∼14 kcal/mol calculated at the CCSD(T)/CBS//B3LYP/6-311++G(3df,2p) level. Hence, although the ammonia molecule still has one lone pair of electrons, carbon monoxide is more reactive toward free propargyl radicals.

In order to investigate the effect of pressure on the kinetics of propargyl radical addition to <span class="Chemical">carbon monoxide, the different pressures P = 1, 10, 100, 7600, and 76,000 Torr were also employed to compute the rate constants of the four addition reactions under the 300–2000 K temperature range. The k1–k4 values at varying temperatures and pressures are tabulated in Tables S6–S10 in Supporting Information and are graphically plotted in Figures –10.

Figure 6

Rate constants of the C3H3 + CO reaction in the temperature range 300–2000 K at 1 Torr (Ar).

Figure 10

Rate constants of the C3H3 + CO reaction in the temperature range 300–2000 K at 76,000 Torr (Ar).

Rate constants of the C3H3 + CO reaction in the temperature range 300–2000 K at 10 Torr (Ar).

Rate constants of the C3H3 + CO reaction in the temperature range 300–2000 K at 100 Torr (Ar).

Rate constants of the C3H3 + CO reaction in the temperature range 300–2000 K at 7600 Torr (Ar).

It is interesting to note that the calculated rate constants not only depend on temperatures as mentioned above but also strongly depend on pressures, as shown in Figures –10. According to these figures, the second-order temperature-dependent rate coefficients gradually increase with rising pressures, for example, the total values of k1–k4 at T = (500, 1000 K) and P = 1, 10, 100, 760, 7600, and 76,000 Torr are (8.60 × 10–19, 5.56 × 10–17), (5.92 × 10–18, 4.57 × 10–16), (3.20 × 10–17, 3.32 × 10–15), (1.06 × 10–16, 1.67 × 10–14), (2.60 × 10–16, 8.45 × 10–14), and (3.82 × 10–16, 3.11 × 10–13) cm3 molecule–1 s–1, respectively. At any pressure values, the k1 value is still dominant, followed by the k2 and k3 values; the k4 value remains in the last position which is 3–5 orders of magnitude smaller than the k1 value. The deviations of those values in the 300–2000 K interval at 1, 10, 100, 7600, and 76,000 Torr reduce in the ranges of 0.65 × 10–21 to 0.08 × 10–16, 0.77 × 10–21 to 0.09 × 10–15, 0.89 × 10–20 to 0.1 × 10–14, 0.65 × 10–20 to 0.08 × 10–12, and 0.26 × 10–20 to 0.04 × 10–12, respectively.

The linear least-square treatments on the total rate constants of the C3H3 + CO reaction at different pressures between 300 and 2000 K lead to the T-dependent Arrhenius expressions

In this study, the unimolecular rate constants of the decomposition processes of IS1-, IS1-, and <span class="Chemical">IS2 back to the reactants have also been considered. The computed results in the temperature range of 300–2000 K at pressures ranging from 1 to 76,000 Torr are listed in Table S11 and graphically plotted in Figures S6–S11 in Supporting Information. It is evident from the table and figures that the unimolecular rate constants increase with rising temperatures and pressures, ranging from approximately 106 to ∼2 × 1012 s–1, indicating that the initial addition intermediates IS1-, IS1-, and IS2 generated from the C3H3 + CO reaction are rather unstable and would rapidly dissociate back to the reactants especially at elevated temperatures (T ≥ 1000 K) and any pressures.

To check the reliability of our calculations, the unimolecular rate constants of the decompositions of C3H3CO forming products (<span class="Chemical">C3H3 + CO), P2 (CHCCHCO + H), and P4 (CHCO + C2H2) have been computed in the 300–2000 K temperature interval at the high-pressure limit using the MESMER code,[38] in comparison with the previously predicted data reported by Tian et al.,[52] as presented in Table and graphically plotted in Figures –13.

Table 2

Unimolecular Rate Constants (in Units of s–1) of the C3H3CO Decomposition Giving C3H3 + CO, CHCCHCO + H, and CHCO + C2H2 in the 300–2000 K Temperature Range at 760 Torr (Ar), where ka, kb, kc, and kd are the Present Rate Constants of IS3 → R (C3H3 + CO), IS3 → P2 (CHCCHCO + H), IS5 → P2, and IS5 → P4 (CHCO + C2H2), while ka′, kb′, kc′, and kd′ are the Rate Constants of these Channels Calculated by Tian et al.[52]

	ka	ka′	kb	kb′	kc	kc′	kd	kd′
T (K)	IS3 → R	IS3 → R	IS3 → P2	IS3 → P2	IS5 → P2	IS5 → P2	IS5 → P4	IS5 → P4
300	5.87 × 10–23	2.05 × 10–22	8.87 × 10–25	1.98 × 10–25	1.60 × 10–10	2.19 × 10–10	3.22 × 10–15	4.79 × 10–15
400	4.24 × 10–14	1.16 × 10–13	3.17 × 10–15	9.57 × 10–16	2.57 × 10–4	3.38 × 10–4	4.38 × 10–8	5.35 × 10–8
500	8.91 × 10–9	2.09 × 10–8	1.77 × 10–9	6.39 × 10–10	1.34	1.73	8.64 × 10–4	9.36 × 10–4
600	3.19 × 10–5	6.79 × 10–5	1.23 × 10–5	4.98 × 10–6	4.01 × 102	5.10 × 102	6.46 × 10–1	6.46 × 10–1
700	1.11 × 10–2	2.20 × 10–2	6.95 × 10–3	3.05 × 10–3	2.34 × 104	2.95 × 104	7.43 × 101	6.99 × 101
800	9.00 × 10–1	1.70	8.16 × 10–1	3.80 × 10–1	4.92 × 105	6.16 × 105	2.64 × 103	2.37 × 103
900	2.76 × 101	5.00 × 101	3.36 × 101	1.63 × 101	5.24 × 106	6.53 × 106	4.28 × 104	3.71 × 104
1000	4.29 × 102	7.51 × 102	6.62 × 102	3.33 × 102	3.47 × 107	4.31 × 107	4.01 × 105	3.38 × 105
1100	4.06 × 103	6.92 × 103	7.64 × 103	3.95 × 103	1.62 × 108	2.01 × 108	2.52 × 106	2.07 × 106
1200	2.65 × 104	4.42 × 104	5.89 × 104	3.11 × 104	5.87 × 108	7.27 × 108	1.17 × 107	9.42 × 106
1300	1.30 × 105	2.12 × 105	3.34 × 105	1.80 × 105	1.74 × 109	2.15 × 109	4.31 × 107	3.41 × 107
1400	5.07 × 105	8.18 × 105	1.48 × 106	8.09 × 105	4.40 × 109	5.44 × 109	1.32 × 108	1.03 × 108
1500	1.66 × 106	2.64 × 106	5.41 × 106	2.99 × 106	9.83 × 109	1.22 × 1010	3.51 × 108	2.70 × 108
1600	4.68 × 106	7.35 × 106	1.68 × 107	9.41 × 106	1.9983 × 1010	2.4683 × 1010	8.27 × 108	6.28 × 108
1700	1.17 × 107	1.82 × 107	4.60 × 107	2.60 × 107	3.6983 × 1010	4.5683 × 1010	1.77 × 109	1.33 × 109
1800	2.64 × 107	4.07 × 107	1.13 × 108	6.41 × 107	6.3983 × 1010	7.9083 × 1010	3.48 × 109	2.58 × 109
1900	5.49 × 107	8.39 × 107	2.52 × 108	1.44 × 108	1.04 × 1011	1.29 × 1011	6.38 × 109	4.70 × 109
2000	1.06 × 108	1.61 × 108	5.20 × 108	2.99 × 108	1.62 × 1011	2.01 × 1011	1.1083 × 1010	8.06 × 109

Figure 11

Rate constants of the IS3 (CHCCHCHO) → C3H3 + CO channel in the temperature range 300–2000 K at a high-pressure limit.

Figure 13

Rate constants of the IS5 (CHCHCHCO) → P2 (CHCCHCO + H) and P4 (CHCO + C2H2) channels in the temperature range 300–2000 K at a high-pressure limit.

Rate constants of the IS3 (CHCCH<span class="Chemical">CHO) → C3H3 + CO channel in the temperature range 300–2000 K at a high-pressure limit.

Rate constants of the IS3 (CHCCH<span class="Chemical">CHO) → P2 (CHCCHCO + H) channel in the temperature range 300–2000 K at a high-pressure limit.

Rate constants of the IS5 (CHCHCHCO) → P2 (<span class="Chemical">CHCCHCO + H) and P4 (CHCO + C2H2) channels in the temperature range 300–2000 K at a high-pressure limit.

The multireflection effect[53,54] has also been considered in the RRKM rate constant calculations for the channels proceeding via multiwells. The input file for rate constant calculation using the MESMER program is provided in Supporting Information. As can be seen in these tables and figures, the unimolecular rate coefficients of the mentioned channels increase quickly with rising temperatures, and our values are in good agreement with those of Tian et al.; for example, the CHCCHCHO → C3H3 + CO rate constants in this work at 300 and 2000 K are 2.05 × 10–22 and 1.61 × 108 s–1, respectively, whereas those of Tian et al. are 5.87 × 10–23 and 1.06 × 108 s–1, respectively. The RRKM calculated rate coefficients shown in Table were fitted to the modified Arrhenius equation, k(T) = A·T·exp(−Ea/RT), yielding the following expressionswhere ka(T), kb(T), kc(T), and kd(T) are the first-order rate constants of the channels of CHCCHCHO → C3H3 + CO (RA), CHCCHCHO → CHCCHCO + H (P2), CHCHCHCO → CHCCHCO + H (P2), and CHCHCHCO → CHCO + C2H2 (P4), respectively. The deviations between the unimolecular rate coefficients in this work and those of Tian et al.[52] in the 300–2000 K range for ka/ka′, kb/kb′, kc/kc′, and kd/kd′ are only 3.5–1.52, 0.22–0.58, 1.37–1.24, and 1.49–0.73, respectively, where ka′, kb′, kc′, and kd′ are the rate constants of Tian et al. for the corresponding reaction channels mentioned above.

Concluding Remarks

In the present computational work, the quantum-chemical mechanism and the rate constant calculation have been performed on the formation and dissociation reactions of the C4H3O radical. All the species (reactants, intermediate states, transition states, and products) on the C3H3 + CO PES have been optimized by DFT at the B3LYP level in conjunction with the Pople 6-311++G(3df,2p) basis set. The single-point energies for these species have been refined at the CCSD(T) level with the CBS limit. The predicted PES reveals that the reaction of C3H3 with CO can occur via addition directions giving rise to three main products, namely, IS1- (CHCCH2CO), IS1- (CHCCH2CO), and IS2 (CH2CCHCO). These reaction channels have to surpass via the energy barriers TS1–TS4 located 13.3, 14.0, 14.3, and 15.9 kcal/mol, respectively, above the entrance channel.

The rate constants of the C3H3 + CO addition reaction have been estimated under the temperature range of 300–2000 K and the 1–76,000 Torr (Ar) pressure range. The calculated results at 760 Torr indicate that the k1 rate constant of the <span class="Chemical">C3H3 + CO → IS1-cis channel is dominant over the 300–2000 K temperature range, ranging from 1.53 × 10–20 to 1.04 × 10–13 cm3 molecule–1 s–1 with a product yield of 62–44%, followed by the values of k2 and k3 rising from 7.8 × 10–21 to 7.73 × 10–14 (6.7–23%) and from 1.66 × 10–21 to 5.5 × 10–14 (∼31.5–34%) cm3 molecule–1 s–1, respectively, while the k4 value of the C3H3 + CO → IS2 channel is so small that can be ignored in the kinetic consideration of the addition between C3H3 and CO. The calculated results have also indicated that the bimolecular T-dependent rate constants increase with rising pressures in the range studied. Moreover, the high-pressure limit rate constants of the C4H3O decomposition forming (C3H3 + CO), (CHCCHCO + H), and (CHCO + C2H2) have been found to agree closely with the theoretically calculated values provided by Tian et al. The predicted unimolecular rate coefficients in the ranges of T = 300–2000 K and P = 1–76,000 Torr also indicated that the intermediate products IS1-, IS1-, and IS2 are rather unstable and would rapidly decompose back to the reactants (C3H3 + CO), especially at high temperatures (T > 1000 K). Therefore, it can be said that the C3H3 + CO reaction is considered to be insignificant at high-temperature regions. At low-temperature/-pressure conditions, the three adducts IS1- (CHCCH2CO), IS1- (CHCCH2CO), and IS2 (CH2CCHCO) are the dominant intermediate products of the addition reaction between the propargyl radical and carbon monoxide.